Question

The magnetic moment of a circular coil carrying current \( I \), having radius \( r \) and number of turns \( n \) is proportional to

• A. \( r \)
• B. \( \frac{1}{r} \)
• C. \( r^2 \)
• D. \( \frac{1}{r^2} \)

Hint:

The magnetic moment of a circular coil is proportional to the area of the coil, which is proportional to \( r^2 \) for a circular coil.

Answer 1

The Correct Option is C

Step 1: Magnetic moment of a coil.
The magnetic moment \( M \) of a circular coil is given by: \[ M = n \cdot I \cdot A \] where \( n \) is the number of turns, \( I \) is the current, and \( A \) is the area of the coil. The area of the coil is \( A = \pi r^2 \), where \( r \) is the radius of the coil.
Step 2: Proportionality of magnetic moment.
Thus, the magnetic moment is proportional to \( r^2 \), corresponding to option (C).
Step 3: Conclusion.
The magnetic moment is proportional to \( r^2 \), corresponding to option (C).